Learning Learning/Parable 3

From OLPC

The sequence QWERTY on the keyboard symbolizes how technology can serve not as a force of progress but for keeping things stuck. The arrangement of keys we all use has no rational explanation, only a historical one: there are other arrangements that are more efficient and easier to learn. Indeed the QWERTY keyboard (as it is called) was deliberately designed to be inefficient. In the early days of the typewriter fast typing caused keys to jam! The idea was to minimize the collision problem by separating those keys that frequently followed one another closely. Just a few years later, general improvements in the technology removed the jamming problem, keys no longer stuck but QWERTY did.

In my book Mindstorms I introduced the term “QWERTY phenomenon” to describe situations in which a design decision made to solve a transient problem stays with us long after the problem has gone away. The most damaging of these is the design of the school curriculum. Like the QWERTY keyboard, it was designed to deal with problems that were real once upon a time, specifically before mechanical technologies gave way to electronic ones. In those days you could make a case for spending so much time at school programming children to do the kinds of calculations a digital device could do far better. You could also justify making arithmetic a central part of elementary education on the grounds that everyone should learn to understand some mathematics and crunching numbers was one of the few candidates to serve as entry-level mathematics. The computer makes available many more paths into mathematical knowledge. In those days you almost HAD to begin a mathematical education by doing arithmentic, because it was one of the few branches of mathematics accessible to children using pencil and paper technologies. It made no sense to try to teach algebra or coordinate geometry to seven-year olds. The concepts of “variable” and “x-coordinate” were far too abstract.

But this has changed dramatically. All of a sudden the computer gives these concepts a form that is even more concrete than rules for adding multi-digit or fractional numbers. For children who have learned to write a program to draw a shape (which children can do in a well designed programming language), a variable is a way to make the program draw the same shape in many different sizes. For children who have learned to write a program, such as a game, that makes an object on the screen move about, coordinates are a way to control where it moves. These concepts cease to be abstract when they become tools to serve immediate personal purposes. Even at a more advanced age most children take a long time to see the point of algebra as it is traditionally presented – and many never do.

Some people might object that it is useless to have children understand algebra when they don’t know how to multiply 78543 by 17629. I have four answers. Take your pick – each one is sufficient for my point. First, algebra captures a way of thinking that is far more important in life (both practical life and intellectual life) than multiplying big numbers. Second, a calculator multiplies better. Third, if it is necessary to know how to multiply this can be learned far more quickly and far less painfully after learning how to think mathematically. The fourth answer, and perhaps the most important, is expressed in the words of my mentor, the late Bob Davis who used to say: “School math teaches the art of getting the right answer without thinking.” Intensive practice of mechanical skills before one knows enough to fully understand them is a great inhibitor of creative thinking.

Last week I used learning a language as an example of how technology could liberate teaching from limitations of the teacher. I was imagining a teacher who had the wonderful human gift of understanding children but happened not to be able to pronounce English. A very similar limitation prevents dedicated teachers from cultivating in children a genuine understanding and love for mathematics. Many teachers who have a deep love for mathematics, and a deep understanding of how it works, develop the knack of helping children cultivate these habits of mind. But many are unable to do this. Perhaps in the age of genuine digital learning everyone will become a math-lover. But again perhaps many will choose not to do so – just as many may not want to learn English. My point is that in the age of technology whether teachers know how to pronounce English or mathematics need not limit their students’ development either as mathematicians or as English speakers.